One-pass and tree-shaped tableau systems for TPTL and TPTLb+Past

Linear Temporal Logic (LTL) is one of the most commonly used formalisms for representing and reasoning about temporal properties computations. Its application domains range from formal verification to artificial intelligence. Many real-time extensions LTL have been proposed over years, including Timed Propositional (TPTL), that makes it possible constrain ordering pairs events as well exact time elapsed between them. The paper focuses on TPTL Bounded with Past (), a bounded variant enriched past operators, which has recently introduced formalise meaningful class timeline-based planning problems. allows refer while keeping computational complexity under control: in contrast full (TPTL+P), whose satisfiability problem non-elementary, -complete. deals by providing an original tableau system each them suitably generalises Reynolds' one-pass tree-shaped LTL. First, we show how handle devising (LTL+P). Then, adapt , proofs soundness completeness resulting systems. In particular, proved exploiting novel model-theoretic argument that, compared originally employed system, provides deeper understanding crucial role prune rule system.